Asymmetric high speed Digital Subscriber Line (ADSL) and Very high speed Digital Subscriber Line (VDSL) are examples of modern communication systems which permit transmission of data over communication lines at very high rates, e.g., up to 52 Mbits/s. One example of a high speed data application is video on demand. The transmission of high-speed data over band-limited channels may be accomplished through the use of DMT-based, digital communications systems. DMT modems follow the general principle of transmitting data by is dividing it into several interleaved bit streams, and using these bit streams to modulate several carriers.
A significant limitation in high data rate communication systems is intersymbol interference (ISI). One way to compensate for ISI in a DMT system is to add a cyclic prefix (guard time) to the beginning of each transmitted DMT symbol. Unfortunately, while increasing the length of prefixes reduces ISI, it also decreases the effective data rate. Another approach to combating ISI is to employ an equalizer at the receiver, but many equalizers require considerable and ongoing computation "overhead." There is a need, therefore, to keep the cyclic prefix length as small as possible and still compensate for ISI using an equalization technique that does not require complicated and ongoing computations.
For purposes of this application, equalization is the process of correcting or compensating for the ISI caused by the communications channel. In practical communications, the frequency response of the channel is not known. Accordingly, an equalizer is designed using numerous parameters that must be adjusted on the basis of measurements of a channel's signal-affecting characteristics.
A transversal filter having a delay line with taps spaced by T-seconds (where T is the sampling interval and f.sub.s =1/T is the sampling rate at the receiver) is a common choice for an equalizer. The outputs of the filter taps are multiplied by a filter coefficient, summed, and fed to a decision device. The tap coefficients correspond to the channel parameters and represent to some extent a "model" of the channel. If the coefficients are properly selected, the equalizer significantly attenuates or practically removes the interference from symbols that are adjacent in time to the desired symbol. The selection of the coefficient values is typically based on minimization of either peak distortion or mean-squared distortion. The coefficients are selected so that the equalizer output is forced towards zero at N sample points on either side of the desired pulse.
There are two general types of automatic equalization. The first equalization approach transmits a training sequence that is compared at the receiver with a locally-generated or otherwise known training sequence. The differences between the two sequences are used to set the equalizer filter coefficients. In the second approach, commonly referred to as adaptive equalization, the coefficients are continually and automatically adjusted directly from the transmitted data. A drawback of adaptive equalization is its computational "cost" involved in continually updating the filter coefficients so that the channel model is adapted to the current conditions of the channel. Equalizer coefficient computational methods employing adaptive algorithms such as the least mean square (LMS) or recursive least square (RLS) are computationally expensive. At a very high sampling rate for high data rate communications system, this kind of continual LMS updating of the equalizer filter coefficients is particularly expensive.
The present invention seeks to reduce both computational cost and cyclic extension, but at the same time effectively equalize received signals to compensate for ISI using a short length equalizer. For many communication applications, such as VDSL and ADSL, the communications channel does not change that much during a particular transmission. In this context of relative "constant" channel conditions, it is satisfactory to estimate the channel coefficients during an initial training sequence before the message is transmitted without thereafter adjusting the filter coefficient values during the transmission. Of course, it may be necessary to monitor channel quality during the transmission, and if channel quality decreases below a certain threshold, the equalizer coefficients could then be updated.
The present invention provides an optimal procedure for determining in the time domain equalizer coefficients for an equalizer, where the equalizer compensates received signals that are distorted by passing through the channel. A unit pulse is transmitted over the communications channel, and a channel impulse response is estimated from the received signal. A cost function establishes a mean-square error associated with the unequalized channel impulse response as compared to a desired impulse response signal. The value of the cost function varies based upon an offset value between the estimated channel impulse response and an equalized channel impulse response. Values of the cost function are determined for different offsets, and the offset that produces the smallest cost function value (corresponding to the minimum mean-square error) is selected. The optimal equalizer coefficients are then calculated using the selected offset and the established cost function.
In a preferred embodiment, the invention is applied to multicarrier modulation systems. Moreover, the cost function is defined as a krakovian function that depends on the offset value. That krakovian function includes a first krakovian which uses the channel impulse response and a second krakovian which uses the autocorrelation of the channel impulse response. Using the first and second krakovians and the selected offset corresponding to the minimal value of the established cost function, the optimal equalizer coefficients are determined in a straightforward, one step calculation.
A better understanding of the features and advantages of the present invention will be obtained by reference to the following detailed description of the invention and the accompanying drawings which set forth an example embodiment in which the principles of the invention are utilized.